Combination of aN${}^3$LO PDFs and implications for Higgs production cross-sections at the LHC

Abstract

We discuss how the two existing approximate N${}^3$LO (aN${}^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN${}^3$LO PDFs with N${}^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN${}^3$LO PDF sets entering the combination. The combined aN${}^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology.

Comments: 22 pages, 11 figures, LHAPDF grids available from https://zenodo.org/records/13843626, matches published version